Question

Find the value of x

What is the answer?

Answer 1

Given data:-

• $5^{2x+1} \div 25 = 125$

To Find:-

• Value of x.

Rules used:-

• If we divide two exponents with the same base then their powers will subtract.

Solution:-

$⟹5^{2x+1} \div 5² = 5³$

$⟹5^{2x+1-2} = 5³$

Comparing exponents,

$⟹2x+1-2= 3$

$⟹2x-1 = 3$

$⟹2x=3+1$

$⟹x = \dfrac{4}{2}$

${\boxed{⟹x = 2}}$

Hence, The Value of x is 2.

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More to know:-

• When two exponential terms with the same base are multiplied, their powers are added while the base remains the same.

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Answer 2

Given

• $\sf{ {5}^{2x + 1} \div 25 = 125 }$

To Find

• Value of x

Solution

$~~~~~:\implies \sf~~~{5}^{2x + 1} \div 25 = 125$

$~~~~~:\implies \sf~~~{5}^{2x + 1} \div {5}^{2} = {5}^{3}$

$~~~~~~~~~~~~~~~~~\boxed{\bf{ \gray{a^m ÷a^n= a^{m-n}} }}$

$~~~~~:\implies \sf~~~{5}^{2x + 1 - 2} = {5}^{3}$

$~~~~~:\implies \sf~~~{5}^{2x - 1} = {5}^{3}$

On comparing both sides we get

$~~~~~:\implies \sf~~~2x - 1 =3$

$~~~~~:\implies \sf~~~2x =3 + 1$

$~~~~~:\implies \sf~~~2x =4$

$~~~~~:\implies \bf{\underbrace{~~~x =2~~~}}$

Laws of Exponents

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf \bigstar{a}^{m} \times {a}^{n} = {a}^{m + n} \: \: \: \: \: \: \: \: \: \: \sf \bigstar{a}^{m} \div {a}^{n} = {a}^{m - n} \\ \: \: \: \: \sf{\bigstar( {a}^{m} ) ^{n} = {a}^{mn} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigstar a {}^{m} \times {n}^{m} = (ab) ^{m} } \: \: \: \:\\ \: \: \sf\bigstar{a}^{0} = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: {\bigstar\frac{ {a}^{m} }{ {b}^{m} }= \left( \frac{a}{b} \right) ^{m} } \: \: \: \: \: \: \: \:\\\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}$